Star-Representations sur des sous-varietes co-isotropes

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dc.creatorBordemann, M.
dc.creatorGinot, G.
dc.creatorHalbout, G.
dc.creatorHerbig, H. -C.
dc.creatorWaldmann, S.
dc.date2003-09-19
dc.date.accessioned2026-07-07T05:01:18Z
dc.date.available2026-07-07T05:01:18Z
dc.descriptionFor a coisotropic (or first-class) submanifold C of a Poisson manifold X we consider star-products for which the vanishing ideal I of C becomes a left ideal in the deformed algebra thus defining a left module structure on the space of smooth functions on C. We show how this can be deduced from a formality conjecture a la Tamarkin generalized to cochains compatible with C. To this end we first prove a theorem a la Hochschild-Kostant-Rosenberg between the space of compatible multivector fields and compatible multidifferential operators. We then equip the latter with a G-infinity structure, and prove that the obstructions to the formality are controlled by certain cohomology groups which we reduce in the case of C being a subvectorspace of the vectorspace M. In codimension 1 we conjecture -encouraged by low-dimensional examples and Gloessner's representation theorem (1998)- that formality holds. For higher codimensions it is not impossible that obstructions occur which in the symplectic case are linked to the Atiyah-Molino class of a regular foliation.
dc.description36 pages, Latex2e, paper in French
dc.identifierhttps://arxiv.org/abs/math/0309321
dc.identifierhttp://arxiv.org/abs/math/0309321
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68620
dc.subjectQuantum Algebra
dc.subject16E40; 53D55
dc.titleStar-Representations sur des sous-varietes co-isotropes
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